Question

What is the exact value of the expression sqrt(189) - sqrt(21) + sqrt(84) ? Simplify if possible.

Answer 1

do you mean
2(sqrt(10k) )* (5k^2)) ?

Answer 2

\[2\sqrt{10k} \times 5k \sqrt{2} \]

Answer 3

I have some of it, I think..

Answer 4

this can be rewritten as
2 * sqrt(10) * k^(1/2) * 5 * k* sqrt(2)
10*sqrt(10*2) * k^(1/2 + 1)

clear till now?

Answer 5

not clear at all.. my lesson says for me to multiply what's out side the radical first, 2 and 5k to get 10k, then multiply what's in the radical, sqrt{10k} and sqrt{2} to get 20k, then it says to combine, 10k sqrt{20k} and simplify, I just don't know how to simplify it.

Answer 6

alright though one and the same thing

now for simplification you need to combine the integers and variables(k in this case)
so your expression can be written as :
10*k * sqrt(20)* sqrt(k)

clear?

Answer 7

so it would be
\[10 \times k \times \sqrt{20} \times \sqrt{k}\]
?

Answer 8

yes
now 10sqrt(20) * k^(1 + 1/2) for the next step
10sqrt(20)*(k^(3/2)) for the final answer

Answer 9

can you put it in equation form, cause it's confusing me when your putting it like that.

Answer 10

\[10\sqrt{20} k ^{3/2} \]

Answer 11

better still
\[\sqrt{20} = \sqrt{2 \times 2\times 5} = 2 \sqrt{5}\]

Answer 12

can you please help me with mine too

Answer 13

that's not one of the answers.. Do you want me to copy and paste the answers on to here?

Answer 14

so final answer \[20\sqrt{5} k ^{3/2}\]

Answer 15

@vetdoc
does this match?

Answer 16

I have 20 sqrt(5k) but not the 3/2 part

Answer 17

ok i got it how your book is going on with the answer

we had reached
10k * sqrt(20k)
\[\sqrt{20k} = \sqrt{2 \times 2 \times 5 \times k} = 2 \sqrt{ 5 k}\]

Answer 18

so final answer\[10k \sqrt{20k} = 10k \times 2 \sqrt{5k} = 20k \sqrt(5k)\]

Answer 19

sqrt(5k)
square root of 5k

Answer 20

okay.. I got it. Thanks

Answer 21

great
:)